Methods for calculating errors of a function whose arguments have individual errors.

learn more… | top users | synonyms

0
votes
0answers
9 views

How to properly consider uncertainty propagation in random variables

I have 34 input random variables and one output random variable, named R. From 33 input random variables and some dataset I determined the best predictive ...
0
votes
0answers
9 views

Error estimation in peak location determination by centroid method

I am trying to locate peak in a data set by numerically calculating the peak using centroid method. How can I estimate the error associated with this peak determination?
5
votes
2answers
125 views

Background subtraction for signal and error analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
0
votes
0answers
47 views

Error for combining multiple binomial distributions

This problem is somewhat involved and I have a partial solution so bear with me. I will illustrate the problem with an example. Lets say we have two processes and we want to know which has a higher ...
2
votes
0answers
41 views

Propagation of Poisson Confidence Intervals

I have a set of measurement with 95% Poisson confidence intervals, and I would like to subtract and multiply them and propagate the error. For example, I measured the copy number of a piece of DNA in ...
1
vote
0answers
270 views

Standard deviation of normalized data

I have a data set $y_i$ (where the $y_i$ are photon counts in time period $i$, $i=1,2,...,n$, assumed Poisson), with an estimated standard error $s_i$ (= $\sqrt{y_i}$) for each count. For some ...
0
votes
1answer
24 views

Error Propagation Calculation

I have a few machines that are used to calibrate each other. Machine 1 has is accurate to 0.025% Machine 1 is used to calibrate Machine 2, which has an accuracy of 0.005% Machine 2 is used to ...
3
votes
0answers
54 views

How do I propagate error when X+Y=1 and aX+bY=1?

I have data for proportions of two diet categories X and Y (from gut samples, n=10) that must sum to 1. I am multiplying each by a different constant (a and b) and then re-calculating the two ...
0
votes
2answers
72 views

Statistical error and error propagation

I have a quantity defined as: $P_{frac} = \frac{F_{max}-F_{min}}{F_{max}+F_{min}}$ I also have the value for $F_{max}$, $F_{min}$, and their statistical errors. How can I calculate the error for ...
0
votes
0answers
70 views

Error propagation calculation yielding negative variance

I am trying to calculate the standard deviation of the sum X = A + B. A and B are mean values, and I do not have access to the source data. A is 0.46 with an SD of 0.014 (SDa) and B is 0.375 with an ...
1
vote
1answer
101 views

How to compare two groups of empirical distributions?

I am working with EEG and now I am trying to compare coherence for two groups of individuals. Problem is coherence is dependent on length of signal but I have signals with different length for each ...
1
vote
1answer
58 views

Reusing predicted values as independent variables for new linear regression

Edit I've rephrased this question severely. Suppose I have a fitness center, and instead of a monthly fee, the people are paying for courses they are taking. I've got the monthly total revenue of all ...
1
vote
1answer
114 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
1
vote
0answers
40 views

Regression with error in covariates

I am looking for some advice for a colleague who is dealing with regression models for which it is know, that the continuous covariate of interest $X_1$ was measured with error. More precisely, we ...
0
votes
1answer
98 views

Possible Paradox: Calculating a confidence interval with within-experiment error

This is a spinoff of How to calculate the confidence interval of the mean of means? and related to When making inferences about group means, are credible Intervals sensitive to within-subject ...
7
votes
1answer
329 views

When making inferences about group means, are credible Intervals sensitive to within-subject variance while confidence intervals are not?

This is a spin off of this question: How to compare two groups with multiple measurements for each individual with R? In the answers there (if I understood correctly) I learned that within-subject ...
6
votes
3answers
999 views

How to compare two groups with multiple measurements for each individual with R?

I have a problem like the following: 1) There are six measurements for each individual with large within-subject variance 2) There are two groups (Treatment and Control) 3) Each group consists of ...
3
votes
0answers
182 views

Average over two variables: Why do standard error of mean and error propagation differ and what does that mean?

I'm doing an experiment with a cryostat to determine the critical temperature for lead. To avoid asymmetries, I determine the critical temperature both through heating (going from 2 K to 10 K) and ...
3
votes
1answer
798 views

Multiplication and division of values with geometric standard deviation

What is the geometric standard deviation of a value, which is the result of dividing two independent values, each of which has its own geometric standard deviation ? It is a frequent situation in ...
5
votes
0answers
207 views

Division of two poisson variables

Let's say I have four variables $x_1, x_2, x_3$ and $x_4$ all distributed as Poisson, with means $\lambda_i$, and standard deviations respectively. Now I want to calculate two further variables $y_1= ...
5
votes
1answer
109 views

Error of the sum of complex numbers

I'm analyzing the effect of precision error in optics experiments. One of the relevant quantities is a sum of $N$ complex numbers, each with a complex relative standard error $\epsilon$. How can I ...
0
votes
0answers
60 views

Determining uncertainty propagation for an overdetermined set of equations

I have this problem of the following format. \begin{align*} x_L &= X\left(\frac{dx_L}{dX}\right) + Y\left(\frac{dx_L}{dY}\right) + Z\left(\frac{dx_L}{dZ}\right)\\ &\\ x_R &= ...
0
votes
1answer
130 views

Formal errors from non-negative least-squares?

I have seen a couple of similar questions, but none with answers, so perhaps I can formulate this question in a way that will be answerable. I am computing a standard linear regression subject to a ...
7
votes
2answers
145 views

Error propagation SD vs SE

I have 3 to 5 measures of a trait per individual in two different conditions (A and B). I'm plotting the average for each individual in each condition and I use the standard error (i.e., ...
1
vote
0answers
33 views

Explaining the difference between error propagation and “grand variance”?

I have the following data concerned with simple radiation detection. I collect a background dose $B$ for 100 seconds and find the standard deviation and get the uncertainty $E_B$. I then take 10 ...
1
vote
2answers
86 views

Calculate effect of independent variable

If $a\times b\times c=t$ and I change $a$, $b$, and $c$, how do I calculate the effect of each change. I believe the equation is: $(a+\Delta a)(b+\Delta b)(c+\Delta c)=(t+\Delta t)$, and then I solve ...
2
votes
0answers
41 views

Combining errors

I've got this tricky problem to solve. Hope somebody can help me. Let's suppose I want to know the mean radius of the trees in a wood. For each tree i I measure the radius at the top, at tha center ...
0
votes
1answer
153 views

Simulating Monte Carlo with different standard deviations and interval confidence

I have a question regarding Monte Carlo simulation (direct simulation), applied to propagation of uncertainties. From what I understand Monte Carlo accepts random numbers of each input variable of ...
1
vote
0answers
37 views

posterior covariance for linear inversion

I am performing a physical experiment where the unavoidably inaccurate setup likely creates errors in the inversion of the data for the model. Let's assume a linear relationship between data $\mathbf ...
5
votes
0answers
327 views

Uncertainty propagation in linear interpolation

How do I calculate the uncertainties in linearly interpolated values from a given tabulated function? I am just coming back into the fold after a bit of a hiatus, and am having trouble ...
0
votes
1answer
37 views

Combining observed Gaussian error with common fractional model error

I'm currently trying to incorporate model errors into a likelihood function to fit the model to some results. Let's just call them $x_{m,i}$ for the model and $x_{o,i}$ for the $N$ observations, ...
1
vote
1answer
101 views

How do I calculate the error propagation of this function?

I'm using a molecular biological method which requires the following normalization $$Q = \frac{A}{\sqrt[k]{\prod_{i=1}^k B_i}}.$$ How can I find the standard deviation of $Q$, given that $A$ and ...
3
votes
0answers
190 views

Error propagation with linear regression

I'm trying to obtain an estimation of the uncertainty related to an analytical method: my function is just a linear regression $f: y=ax+b+ \epsilon$ with $y_i=\frac{R_i}{C}$, both $R$ and $C$ are ...
0
votes
0answers
663 views

Standard error of fold changes

I have a conceptual problem to understand the standard error of the ratio of two random variables after error propagation. Let $X$ and $Y$ be two random variables with means $\bar x$ and $\bar y$ and ...
2
votes
0answers
52 views

Variance in a known population

I am working on a problem that is similar to the standard radioactive decay rate experiment, but with a twist. In the normal experiment, one takes several different measurements of the decay rate, ...
0
votes
0answers
81 views

Error bars on a logarithm

I'm plotting the following point using python (a and b have are non gaussian): x=np.log10(a) y=np.log10(b) xmedian=np.median(x) ymedian=np.median(y) and I ...
2
votes
1answer
393 views

Propagation of uncertainty through a linear system of equations

If I have a system of equations, $Ax=B$ where the elements of $B$ have been experimentally determined and as such each element has some uncertainty, how would I propagate this to the elements of $x$? ...
0
votes
1answer
263 views

Mean of means -> error propagation or uncertainty or both?

my problem is as follows. I have a simulation of a neural network which creates activity patterns, learns them and then tries to retrieve previously learned patterns one by one. The performance of ...
0
votes
1answer
196 views

Propagation of errors with median absolute deviation from the median?

Is there a theoretically-sound way to perform propagation of errors with robust statistics? I am trying to characterize the errors inherent in a measurement and propagate the uncertainty through ...
1
vote
2answers
89 views

Propagation of errors using simulation

If I construct confidence intervals for a calculation based on simulating inputs rather than using error propagation formulas, would this be considered as belonging to 'Monte Carlo' methods? I would ...
1
vote
1answer
70 views

statistical error on difference f(x) - x

Suppose I've a random variable $X$ and a sample of it with size $N$. I count how many element of the sample fall in a specific range $a<x<b$ and I found $n$ entries, so if I use Poisson ...
1
vote
1answer
232 views

Propagation of uncertainty through an average

I have a set of distance measurements that are all accurate to +/- 0.01 M. {1.00,2.00,3,00} We can obtain the distance moved ...
2
votes
1answer
331 views

Uncertainty on parameter of unknown function

I have a collection of data points, which are counts as a function of length. Each data point is the result of many trials and has an error bar. The function ...
3
votes
1answer
333 views

Median Averaging and Error Analysis

I am not sure if i should be asking this on the Mathematics of Physics Stack Exchange site. I am taking data for a physics research application and have a question about using median vs. mean ...
1
vote
1answer
81 views

Error propagation and under-represented variable

I am running a relatively simple propagation of error analysis on an equation: $$S = \frac{ABC}{XY}$$ I have independent random error terms calculated for each variable (for the purposes of this ...
1
vote
0answers
80 views

Error estimation and propagation

Suppose I pull from literature a relationship between $X$ and $Y$ with reported confidence intervals from a linear regression $$Y = 2\ (\pm .5) + 5\ (\pm .2)X$$ and then another relationship between ...
1
vote
0answers
47 views

Error of generalized classifier performance

I am working on a problem where it is expensive to label data and I have sampled a small subset of the available data and labeled it. My classifier is a binary classifier that I use with the hope of ...
2
votes
1answer
99 views

Systematic vs. statistical error

I'm currently working with some measurements of the following form: Three test subjects, three trials per test subject, three measurement points per trial: At each measurement point within each ...
3
votes
0answers
158 views

Error propagation from fit parameters

I have two distinct data samples($A$ and $B$), and to each one a gaussian is fitted. I then evaluate the product $S = \sigma_A * \sigma_B$ ($\sigma_A$ and $\sigma_B$ and their errors are obtained ...
5
votes
2answers
529 views

Combining experimental error in a mean

I understand the rules for combining experimental errors in sums, differences and ratios (as explained here), but what happens to an experimental error when you average it? Say, ruler measurements of ...